<p>This work presents first-principles calculations of long-range intermolecular dispersion energies between two atoms or molecules as expressed in terms of the C₆ dipole-dipole dispersion coefficients. In a series of publications, it has been shown by us that the complex linear polarization propagator method provides accurate <em>ab initio</em> and first-principles density functional theory values of the C₆ dispersion coefficients in comparison with those reported in the literature. The selected samples for the investigation of dispersion interactions in the electronic ground state are the noble gases, <em>n</em>-alkanes, polyacenes, azabenzenes, and C₆₀. It has been shown that the proposed method can also be used to determine dispersion energies for species in their respective excited electronic states. The C₆dispersion coefficients for the first <em>π</em> → <em>π*</em> excited state of the azabenzene molecules have been obtained with the adopted method in the multiconfiguration self-consistent field approximation. The dispersion energy of the <em>π</em> → <em>π*</em> excited state is smaller r than that of the ground state. It is found that the characteristic frequencies ω₁ defined in the London approximation of <em>n</em>-alkanes vary in a narrow range and that makes it possible to construct a simple structure-to-property relation based on the number of -bonds for the dispersion interaction in these saturated compounds. However, this simple approach is not applicable for the interactions of the <em>π</em>-conjugated systems since their characteristic frequencies <em>ω</em>₁ vary strongly depending on the systems.</p> / Report code: LIU-TEK-LIC-2006:2

This work presents first-principles calculations of long-range intermolecular dispersion energies between two atoms or molecules and of electronic circular dichroism spectra of chiral molecules. The former is expressed in terms of the C6 dipole-dipole dispersion coefficients Δε, and the latter is given in terms of the extinction coefficient. In a series of publications, the complex linear polarization propagator method has been shown to be a powerful tool to provide accurate ab initio and first-principles density functional theory results. This was the case not only for the C6 dispersion coefficients but also for the electronic circular dichroism at an arbitrary wavelength ranging from the optical to the X-ray regions of the spectrum. The selected samples for the investigation of dispersion interactions in the electronic ground state are the noble gases, n-alkanes, polyacenes, azabenzenes, alkali-metal clusters, and C60. It is found that the values of C6 for the sodium-cluster-to-fullerene interactions are well within the error bars of the experiment. The proposed method can also be used to determine dispersion energies for species in their respective excited electronic states. The C6 dispersion coefficients for the first π → π* excited state of the azabenzene molecules have been obtained with the adopted method in the multiconfiguration self-consistent field approximation. The dispersion energy of the π → π* excited state is smaller than that of the ground state. It is found that the characteristic frequencies ω1 defined in the London approximation of n-alkanes vary in a narrow range which makes it possible to construct a simple structure-to-property relationship based on the number of π-bonds for the dispersion interaction in these saturated compounds. However, this simple approach is not applicable to the interactions of the π-conjugated systems since, depending on the systems, their characteristic frequencies ω1 can vary greatly. In addition, an accomplishment of calculations of the electronic circular dichroism spectra in the near-edge X-ray absorption has been demonstrated.

This work presents first-principles calculations of long-range intermolecular dispersion energies between two atoms or molecules as expressed in terms of the C6 dipole-dipole dispersion coefficients. In a series of publications, it has been shown by us that the complex linear polarization propagator method provides accurate ab initio and first-principles density functional theory values of the C6 dispersion coefficients in comparison with those reported in the literature. The selected samples for the investigation of dispersion interactions in the electronic ground state are the noble gases, n-alkanes, polyacenes, azabenzenes, and C60. It has been shown that the proposed method can also be used to determine dispersion energies for species in their respective excited electronic states. The C6 dispersion coefficients for the first π → π* excited state of the azabenzene molecules have been obtained with the adopted method in the multiconfiguration self-consistent field approximation. The dispersion energy of the π → π* excited state is smaller r than that of the ground state. It is found that the characteristic frequencies ω1 defined in the London approximation of n-alkanes vary in a narrow range and that makes it possible to construct a simple structure-to-property relation based on the number of -bonds for the dispersion interaction in these saturated compounds. However, this simple approach is not applicable for the interactions of the π-conjugated systems since their characteristic frequencies ω1 vary strongly depending on the systems. / <p>Report code: LIU-TEK-LIC-2006:2</p>

We have investigated the noncovalent interactions in carbohydrate-aromatic interactions which are pivotal to the recognition of carbohydrates in proteins. We have employed quantum mechanical methods to study carbohydrate-aromatic complexes. Due to the importance of dispersion contribution to the interaction energy, we mainly use density functional theory augmented with an empirical correction for the dispersion interactions (DFT-D). We have validated this method with a limited number of high level ab initio calculations. We have also analysed the vibrational and NMR chemical shift characteristics using the DFT-D method. We have mainly studied the complexes involving β-glucose with 3-methylindole and p-hydroxytoluene, which are analogues of tryptophan and tyrosine, respectively. We find that the contribution for interaction energy mainly comes from CH/π and OH/π interactions. We find that the interaction energy of complexes involving CH/π and OH/π interactions is reflected in the associated blue and red shifts of vibrational spectrum. We also find that the interactions involving 3-methylindole are somewhat greater than those for p-hydroxytoluene. The C-H blueshifts are also in parallel with the predicted NMR proton shift. We have also tested different density functionals including both standard density functionals and newly developed M0x functionals and MP2 method for studying carbohydrate-aromatic complexes. The DFT-D method and M06 functionals of the M0x family are found to perform better, while B3LYP and BLYP functionals perform poorly. We find that the inclusion of a dispersion term to BLYP is found to perform better. The dispersion energy dominates over the interaction energy of carbohydrate-aromatic complexes. From the DFT-D calculations, we found that the complexes would be unstable without the contribution from dispersive energy. We have also studied the importance of noncovalent interactions in functionalization of nanotubes by nucleic acid bases and aromatic amino acids by using semi-empirical methods with dispersion term such asPM3-D and PM3-D*. We find that the both semi-empirical schemes give reasonable interaction energies with respect to DFT-D interaction energies. We have also used PM3-D method to study the adsorption of organic pollutants on graphene sheet and on nanotubes. We found that the semi-empirical schemes, which are faster and cheaper, are suitable to study these larger molecules involving noncovalent interactions and can be used as an alternative to DFT-D method. We have also studied the importance of dispersion interaction and the effect of steric hindrance in aggregation of functionalized anthracenes and pentacenes. We have also employed molecular dynamics simulation methods to study the aggregation of anthracene molecules in toluene solution.

Die vorliegende Arbeit befasst sich mit dem Thema der Nichtgleichgewichts-Dispersionskräfte. Der Fokus liegt auf der kontroversen Casimir- bzw. Quantenreibung. Sie tritt auf, wenn sich zwei elektrisch neutrale Körper relativ zueinander bewegen. Vermittelt wird diese kontaktlose Reibungskraft über fluktuierende elektromagnetische (Quanten-) Felder und ist somit der Kategorie der fluktuationsinduzierten Phänome zuzuordnen, deren bekannte Beispiele die Van-der-Waals-Kraft und der Casimir-Effekt sind. Im Speziellen wurde die Situation eines mikroskopischen Objektes, welches sich mit einer festgelegten Geschwindigkeit und Höhe über eine makroskopische und flache Oberfläche beweget, untersucht. Um einen Zugang in das Themenfeld zu erlangen, wird eine kurze Einleitung in die Theorie der linearen Antwort und der Dynamik offener Systeme gegeben. Des Weiteren, werden unterschiedliche Modelle zur Beschreibung des mikroskopischen Objektes eingeführt und verschiedene Konfigurationen und Modelle bezüglich der makroskopischen Oberfläche berücksichtigt. Neben einem exakten, wenn auch komplexen, Integralausdruck werden diverse asymptotische Ausdrücke für verschiedene relevante Grenzfälle der kontaktlosen Reibung hergeleitet. Darüber hinaus, um die Asymptoten mit der exakten Lösung vergleichen zu können, wurde eine numerisch Auswertungsroutine des exakten Ausdrucks entwickelt und implementiert. Durch die Nutzung einer vollen Nichtgleichgewichtbeschreibung und das Einbeziehen sowohl der Rückwirkung des elektromagnetischen Feldes auf die Dynamik des mikroskopischen Objektes, als auch dessen Rotationsfreiheitsgrade, werden bestehende theoretische Beschreibungen erweitert. Abschließend wird ein Ausblick auf experimentelle Messungen der kontaktlosen Reibung gegeben. / The present thesis addresses the topic of nonequilibrium dispersion forces. The focus lies on the controversial Casimir or quantum friction, which occurs when two electrically neutral bodies move at a relative velocity with respect to each other. The noncontact friction force is mediated by the fluctuations of the (quantum) electromagnetic field and therefore belongs to the category of fluctuation-induced phenomena, whose prominent examples are the van der Waals force and the Casimir effect. Especially, the setup of a microscopic object moving at a fixed velocity and height above a flat macroscopic surface is investigated. To access this topic, a brief introduction into linear response and open system dynamics is given. Moreover, different models for the description of the microscopic object are introduced and various setups and models of the flat macroscopic surface are considered. Besides an exact but rather involved integral expression, several asymptotic expressions of the noncontact friction for different relevant limits are derived. Furthermore, in order to compare the asymptotic with the exact expression, a numerical approach for its evaluation was developed and implemented. Using a full nonequilibrium approach, which includes the backaction of the electromagnetic field onto the microscopic object’s dynamics, as well as its rotational degrees, existing theoretical descriptions are extended. Eventually, an outlook towards experimental measurements of the noncontact friction is given.

Wir untersuchen die Dynamik von offenen Quantensystemen sowohl im Gleichgewicht als auch im Nichtgleichgewicht. Unser Fokus liegt dabei auf der quantenoptischen Dispersionswechselwirkung zwischen einem mikroskopischen Teilchen und einer komplexen elektromagnetischen Umgebung. Wir sind der Meinung, dass Langzeitkorrelationen in dem System essenziell zum Verständnis der Dynamik des Teilchens beitragen können. Unter Langzeitkorrelationen verstehen wir die Beiträge zur Autokorrelationsfunktion von Quantenoperatoren, die als ein inverses Potenzgesetz in der Verzögerungszeit skalieren. Das Einbeziehen von Langzeitkorrelationen in unser theoretisches Modell sichert die Selbstkonsistenz unserer Beschreibung und ermöglicht es uns, die Rückkopplung der Umgebung auf das Teilchen vollständig zu berücksichtigen. Darüber hinaus erlaubt es uns die Vorhersage von bisher übersehenen Effekten und Mechanismen, die das Verhalten von Dispersionskräften im Gleichgewicht und Nichtgleichgewicht bestimmen. Unsere Beispiele reichen von der Wechselwirkungsentropie des magnetischen Casimir-Polder-Effekts, über den Einfluss von Materialeigenschaften und geometrischen Überlegungen auf experimentelle Aufbauten, bis hin zur Thermodynamik von Quantenreibung. Wir geben den Leser_innen außerdem eine Orientierungshilfe, wann und wie Langzeitkorrelationen in theoretische Modellbildungen einbezogen werden müssten und welche Auswirkungen im Zusammenhang mit quantenoptischen Dispersionskräften zu erwarten sind. / We explore the dynamics of open quantum systems in both equilibrium and nonequilibrium situations. Our focus lies on the quantum-optical dispersion interaction between a microscopic particle and a complex electromagnetic environment. We argue that long-time correlations in the system can be essential for understanding the dynamics of the particle. We define long-time correlations as those contributions to the autocorrelation function of quantum operators which scale as an inverse power law in the time delay. Incorporating long-time correlations into our theoretical model safeguards the self-consistency of our description and allows us to consider the full back-action of the environment on the particle. Moreover, it leads us to the prediction of previously overlooked effects and mechanisms determining dispersion forces in equilibrium and nonequilibrium. Our examples range from the interaction entropy of the magnetic Casimir-Polder effect, over the impact of material properties and geometric considerations for experimental setups, all the way down to the thermodynamics of quantum friction. We further provide the reader with a guideline when and how to include long-time correlations into theoretical models and what effects can be expected to emerge in the context of quantum-optical dispersion forces.

This thesis considers the problem of determining Casimir-Lifshitz forces in inhomogeneous media. The ground-state energy of the electromagnetic field in a piston-geometry is discussed. When the cavity is empty, the Casimir pressure on the piston is finite and independent of the small-scale physics of the media that compose the mirrors. However, it is demonstrated that, when the cavity is filled with an inhomogeneous dielectric medium, the Casimir energy is cut-off dependent. The local behavior of the stress tensor commonly used in calculations of Casimir forces is also determined. It is shown that the usual expression for the stress tensor is not finite anywhere within such a medium, whatever the temporal dispersion or index profile, and that this divergence is unlikely to be removed by modifying the regularisation. These findings suggest that the value of the Casimir pressure may be inextricably dependent on the detailed behavior of the mirror and the medium at large wave vectors. This thesis also examines two exceptions to this rule: first, the case of an idealised metamaterial is considered which, when introduced into a cavity, reduces the magnitude of the Casimir force. It is shown that, although the medium is inhomogeneous, it does not contribute additional scattering events but simply modifies the effective length of the cavity, so the predicted force is finite and can be stated exactly. Secondly, a geometric argument is presented for determining a Casimir stress in a spherical mirror filled with the inhomogeneous medium of Maxwell's fish-eye. This solution questions the idea that the Casimir force of a spherical mirror is repulsive, but prompts additional questions concerning regularisation and the role of non-local effects in determining Casimir forces.

No description available.

Les descriptions des interactions faibles et notamment de la dispersion représentent un problème majeur pour la théorie de la fonctionnelle de la densité. En effet, le caractère fortement local des fonctionnelles rend problématique la description des interactions à longue-portée. Aussi, plusieurs stratégies sont envisagées: des corrections des fonctionnelles existantes ou une introduction de méthodes post-Hartree-Fock par séparation de portée. Des résultats dans les deux cas sont exposés. Tout d'abord, la méthodologie hybride est appliquée à des dimères de métaux de transition (Cr2, Mn2 et Zn2). Ensuite, le calcul de coefficients de corrections pour la dispersion dans un cadre relativiste est présenté. Enfin, les interactions faibles peuvent également résulter de l'interaction d'une molécule avec un champ magnétique. Dans ce cadre, une modélisation de la modification de la densité électronique dans les systèmes aromatiques sous l'influence d'un champ magnétique extérieur est présentée. / In quantum chemistry description of weak interactions, and particularly dispersion forces, are major problems for density functional theory. The strongly local character of functional does not allow to describe properly the long range interactions. Thus, two different strategies have been considered. Correcting the available functional or introduce post-Hartree-Fock methods by mean of range separation.Results in the two cases are discussed. First, the range separated hybrid methodology is applied to transition metal dimers (Cr2, Mn2 and Zn2). Then, correction coefficients for dispersion are calculated within the relativistic framework. Within this relativistic framework, a modelling of the electronic density in aromatic system under the influence of an external magnetic field is also presented.